An Anisotropic Fourth-Order Diffusion Filter for Image Noise Removal

Fourth-order nonlinear diffusion filters used for image noise removal are mainly isotropic filters. It means that the spatially varying diffusivity determined by a diffusion function is applied on the image regardless of the orientation of its local features. However, the optimal choice of parameters in the numerical solver of these filters for having a minimal distortion of the image features results in forming speckle noise on the denoised image and a very slow convergence rate especially when the noise level is moderately high. In this paper, a new fourth-order nonlinear diffusion filter is introduced, which has an anisotropic behavior on the image features. In the proposed filter, it is shown that a suitable choice for a set of diffusivity functions to unevenly control the strength of the diffusion on the directions of the level set and gradient leads to a good edge preservation capability compared to the other diffusion or regularization filters. The comparison of the results obtained by the proposed filter with those of the other second and fourth-order filters shows that the proposed method produces a noticeable improvement in the quality of denoised images evaluated subjectively and quantitatively.     

基于四阶偏微分方程平滑的图像分割新方法

在方向曲率模值描述图像平滑度的泛函基础上，推导出一种四阶偏微分方程(PDE)图像降噪模型，在有效降噪的同时，较好地保持了边缘。该方法处理结果为分段线性图像，且在目标边缘处梯度存在阶跃。利用降噪结果的这一特点，提出一种新测地线主动轮廓模型。实验表明，新模型不但稳定，轮廓提取能力强，而且收敛速度快。     

Edge preservation of impulse noise filtered images by improved anisotropic diffusion

This paper provides a robust scheme for random valued impulsive noise reduction along with edge preservation by anisotropic diffusion with improved diffusivity. The defective impulse noisy pixels are detected by Laplacian based second order pixel difference operation where these defective pixels are replaced by appropriate values with regard of the gray level of their four directional neighbors. This de-noised image undergoes the diffusion operation where diffusion coefficient function is modified to make it adaptive by incorporating local gray level variance information. The proposed modified diffusion scheme effectively restore the edges and fine details destroyed during impulse noise reduction process. The effect of proposed diffusion scheme has been studied on various images and the results are compared with some existing diffusion methods which are independently used for impulse noise reduction and edge preservation. The results shows that the prior removal of impulsive noise before the application of diffusion process is advantageous over the direct application of diffusion for removing the impulsive noise. In addition, the results of the proposed diffusion scheme are compared with some of the median filter based methods which are effectively used for impulse noise reduction without caring of edge preservation. The proposed diffusion scheme sufficiently preserves the edges without boosting of impulsive noise components on images corrupted up to 50 % of the impulsive noise density.     

一种基于非线性扩散方程的PET重建方法

正电子发射断层重建是一类不适定问题,因此正则化方法常用来抑制噪声提高重建的质量.依据Mumford-Shah泛函模型提出了该类重建问题的统一变分模型.基于这一模型,提出了一种新的基于扩散方程的PET重建算法,同时给出了线性和非线性两种方法.实验结果表明,两种方法均有良好的重建性能,并且非线性方法通过合理的设置参数,能体现出较为优越的抗噪声性能和边缘保持特性.     

Sobolev 广义度量下的各向异性扩散模型

给出了Sobolev空间的一种广义度量, 在该度量下提出了一个新的各向异性增强、扩散方程. 广义度量中的变系数, 较好地控制了方程的扩散行为, 使得新模型不仅能有效增强图像的细节特征, 而且能在噪声去除和边缘保护之间取得较好的平衡, 同时给出了相应的隐式离散算法. 仿真实验结果表明, 新模型和算法是行之有效的.     

PDE模型在声纳图像去噪中的应用研究

偏微分方程方法在光学图像去噪中已有很多成功的应用,但用于声纳图像去噪的情况还不多见。针对声纳图像受噪声污染严重的问题,将偏微分方程原理引入到声纳图像去噪中,重点讨论了两种偏微分方程模型:ROF模型和四阶扩散模型。基于这两种模型对声纳图像进行去噪处理,仿真实验证明了偏微分方程去噪算法的有效性,并对比分析了两种模型的去噪性能。ROF模型适用于低信噪比条件下的声纳图像处理,而四阶扩散模型在高信噪比条件下,能够很好地保持图像边缘,但当噪声污染严重时,其去噪后的SNR比ROF模型去噪低了近10 dB,不利于声纳图像处理。     

Fuzzy based Impulse Noise Reduction Method

In this paper, we propose an image filtering technique based on fuzzy logic control to remove impulse noise for low as well as highly corrupted images. The proposed method is based on noise detection, noise removal and edge preservation modules. The main advantage of the proposed technique over the other filtering techniques is its superior noise removal as well as detail preserving capability. Based on the criteria of peak-signal-to-noise-ratio (PSNR), mean square error (MSE), structural similarity index measure (SSIM) and subjective evaluation measure we have found experimentally that the proposed method provides much better performance than the state-of-the-art filters. To analyze the detail preservation capability of the proposed filter sensitivity analysis is performed by changing the detail preservation module to see its effects on the details (texture and edge information) of resultant image. This sensitivity analysis proves experimentally that significant image details have been preserved by the proposed method.     

基于Mallat-Zhong离散小波变换小波的超声图像各向异性扩散抑噪方法

针对传统各向异性扩散方法在超声图像散斑噪声抑制中存在的噪声抑制不充分与边缘特征保持不足的问题,提出一种基于Mallat-Zhong离散小波变换(MZ-DWT)小波的散斑噪声抑制方法。该方法将MZ-DWT小波分析与期望值最大化(EM)算法作为图像中均匀区域与边缘区域的鉴别因子,使扩散系数能够更准确地控制扩散强度与扩散速度,从而达到充分抑制噪声和保护边缘的目的。实验结果表明,所提方法在有效抑制散斑噪声的同时,更好地保持了图像细节信息,其性能优于传统各向异性扩散方法。     

Image denoising by anisotropic diffusion with inter-scale information fusion

Anisotropic partial differential equations (PDEs) based schemes for denoising digital images are fast becoming an indispensable tool in computer vision problems. In this paper we propose to denoise noisy images via such multiscale anisotropic diffusion. In general, digital images contain objects of multiple scales and denoising them without destroying edges is one of the main objective in early computer vision problems. Unlike the previous approaches, which discard the multiple scale based images produced by anisotropic PDE, we utilize information contained in them. By effectively combining the inter-scale details, the proposed scheme improves upon the noise removal and detail preservation properties over other schemes. Numerical results indicate that the scheme achieves good denoising with edge preservation on a variety of images.     

Ultrasound speckle reduction by a SUSAN-controlled anisotropic diffusion method

An ultrasound speckle reduction method is proposed in this paper. The filter, which enhances the power of anisotropic diffusion with the Smallest Univalue Segment Assimilating Nucleus (SUSAN) edge detector, is referred to as the SUSAN-controlled anisotropic diffusion (SUSAN_AD). The SUSAN edge detector finds image features by using local information from a pseudo-global perspective. Thanks to the noise insensitivity and structure preservation properties of SUSAN, a better control can be provided to the subsequent diffusion process. To enhance the adaptability of the SUSAN_AD, the parameters of the SUSAN edge detector are calculated based on the statistics of a fully formed speckle (FFS) region. Different FFS estimation schemes are proposed for envelope-detected speckle images and log-compressed ultrasonic images. Adaptive diffusion threshold estimation and automatic diffusion termination criterion are employed to enhance the robustness of the method. Both synthetic and real ultrasound images are used to evaluate the proposed method. The performance of the SUSAN_AD is compared with four other existing speckle reduction methods. It is shown that the proposed method is superior to other methods in both noise reduction and detail preservation.     

去除磁共振成像图像莱斯噪声的加权扩散

针对各向同性扩散易于造成图像边缘等特征区域的模糊以及相干增强扩散易于在图像背景区域内产生伪条纹的问题,提出了一种根据磁共振成像（MRI）图像莱斯噪声分布特点来对其进行降噪的加权扩散算法。该算法以MRI图像背景区域的莱斯噪声方差作为区分MRI图像背景区域和感兴趣的边缘特征区域二者特征差异的阈值。基于该阈值,该算法构造了一个加权函数,并用该函数对各向同性扩散和相干增强扩散进行加权。加权函数根据图像在不同结构区域的变化,自适应地调整两种扩散的权值,从而充分发挥两种扩散的优势并克服各自的不足。实验结果表明,该算法在峰值信噪比（PSNR）及平均结构相似度（MSSIM）的评价上优于一些经典算法。因此,该算法的降噪及保护、增强边缘的能力更为优越。     

一种基于人类视觉的模糊边缘敏感去噪方法

为了在消除噪声的同时保留或加强图像中的细节,提出了一种模糊边缘敏感去噪算法.该算法在有关人类视觉系统特性的基础上,结合模糊逻辑技术,判断像素所处的位置,并采用相应的滤波策略以进行噪声消除.实验结果表明,该算法在高斯噪声平滑、脉冲噪声消除以及边缘保留方面,相比其他一些算法,如传统的边缘敏感噪声消除算法以及模糊去噪算法,能提供更好的性能.     

一种基于二阶和四阶PDEs的变分去噪方法

二阶偏微分方程图像去噪方法在去除噪声同时保护边缘效果较好,但在平滑区会产生阶梯效应,而四阶方法可以消除阶梯效应,基于此提出了一种将二阶与四阶偏微分方程相结合的变分去噪方法,给出了其欧拉方程和梯度下降流,并分析了数值离散化方法。通过去噪实验表明,该方法能有效去除噪声干扰,在一定程度上保护边缘,并且可以有效减弱阶梯效应,改善图像质量。     

基于平稳小波域的各向异性扩散图像去噪方法

针对传统的各向异性扩散去噪方法存在的导致图像细节丢失的问题,提出了一种基于平稳小波域的各向异性扩散图像去噪方法。该方法根据平稳小波变换的特性,通过在高频和低频子带上选用不同的梯度门限进行各向异性扩散,然后进行重构得到去噪后的结果图像。实验结果表明,该方法在有效去除噪声的同时,图像细节保留较好,去噪后的图像具有更好的质量。     

Iterative Image Restoration Combining Total Variation Minimization and a Second-Order Functional

A noise removal technique using partial differential equations (PDEs) is proposed here. It combines the Total Variational (TV) filter with a fourth-order PDE filter. The combined technique is able to preserve edges and at the same time avoid the staircase effect in smooth regions. A weighting function is used in an iterative way to combine the solutions of the TV-filter and the fourth-order filter. Numerical experiments confirm that the new method is able to use less restrictive time step than the fourth-order filter. Numerical examples using images with objects consisting of edge, flat and intermediate regions illustrate advantages of the proposed model. This work has been supported by the Research Council of Norway.     

结合异质扩散和小波包分解的医学图像分割算法

提出一种医学图像解剖结构特征提取算法,结合异质扩散和小波包分解实现了医学图像分割.在异质扩散基础上,提出一种新的FAB扩散方法对图像进行去噪,同时保持图像解剖结构的边缘和局部细节;然后用一个基于小波包分解的自适应边缘检测算法来检测图像的解剖结构的轮廓特征.分割结果表明,该方法能在有效地去除噪声的基础上完成医学图像解剖结构轮廓特征的提取.     

改进各向异性扩散模型在图像滤波去噪中的应用

为了增强锅炉水位计图像滤波去噪效果,提高图像清晰度,便于后期液位计图像识别研究,通过分析P-M各向异性扩散模型、选择扩散模型及You Yu-Li和Kaveh M四阶偏微分方程的滤波去噪算法,提出了改进各向异性扩散模型滤波算法.所提算法对Perona和Malik两个扩散函数均值化,并引入标准差作为梯度期望值的偏差裕度,结合了P-M各向异性扩散模型保边缘特性的优点,并消除了由于传统各向异性滤波算法迭代过度所造成的阶梯缺陷问题,确保图像有用信息不缺失和像素点平滑度.实验结果表明:所提算法能够更好地降低噪声对目标信号提取产生的影响,提高了图像识别鲁棒性,增强了图像平滑滤波效果,保证了锅炉水位计图像边缘清晰度和完整性.     

基于视觉掩蔽效应的图像扩散

提出一种基于视觉掩蔽效应的图像扩散算法.结合人类视觉系统的特性,利用图像上下文像素的非均质性度量定义了新的噪声掩蔽函数,可以有效地区分噪声和边缘特征,由此得到的噪声可见度函数作为各向异性扩散的扩散系数.算法同时利用了图像的局部梯度信息和较大邻域的上下文信息,可以在滤除噪声的同时更加有效地保留图像的重要特征,而且避免了传...     

An efficient decision-based and edge-preserving method for salt-and-pepper noise removal

In this paper, we propose an improved two-stage scheme for the removal of salt-and-pepper noise based on an efficient impulse detector and the edge-preserving total variation inpainting model. We test the proposed algorithm on the four images corrupted by salt-and-pepper noise with a wide range of noise levels varied from 10% to 95%, and compare it with the six other well known filters. Further, we evaluate quantitatively the performance of these filters with the peak signal-to-noise ratio (PSNR), the measure of structural similarity (SSIM) and the image enhancement factor (IEF). The experimental results have demonstrated that the proposed filter performs impressively in noise suppression and edge preservation.     

一种基于Contourlets变换和全变差的图像去噪方法

为了在克服振荡现象的同时更多地保留图像细节部分,利用一种新的图像细节表征方法Contourlet变换,在Contourlet框架下嵌入全变差,提出了一种新的非线性无约束最优化图像去噪方法。由于Contourlet变换具有多分辨率分析和多方向的特性,使得在Contourlets域中建立模型比在小波域中建立模型更有优势。实验证明该方法在抑制噪声的同时不仅能够很好地减少阈值产生的振荡现象,同时也能很好地保持图像的边缘,是一种有效的去噪方法。